%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP582-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:57:18 EDT 2022
% Result : Unsatisfiable 1.72s 1.95s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 5 RR)
% Number of literals : 35 ( 34 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(identity,a2) != a2,
file('GRP582-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
file('GRP582-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP582-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP582-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP582-1.p',unknown),
[] ).
cnf(11,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
double_divide(double_divide(a2,identity),identity) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
[iquote('back_demod,1,demod,6')] ).
cnf(13,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.1,10.1.1')] ).
cnf(15,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.2.2,10.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.2,10.1.1')] ).
cnf(21,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2.2,3.1.1')] ).
cnf(22,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(24,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),11,11])]),
[iquote('para_into,19.1.1.1.2.1,10.1.1,demod,11,11,flip.1')] ).
cnf(25,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(identity,C)),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),24,24]),
[iquote('back_demod,22,demod,24,24')] ).
cnf(28,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),24]),
[iquote('back_demod,19,demod,24')] ).
cnf(31,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),24]),
[iquote('back_demod,15,demod,24')] ).
cnf(33,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),24,24]),
[iquote('back_demod,13,demod,24,24')] ).
cnf(37,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(para_from,[status(thm),theory(equality)],[28,11]),
[iquote('para_from,27.1.1,10.1.1.2')] ).
cnf(45,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,24]),24])]),
[iquote('para_into,25.1.1.2.2.2,23.1.1,demod,24,flip.1')] ).
cnf(47,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,11]),45]),
[iquote('para_into,25.1.1.2.2.2,10.1.1,demod,45')] ).
cnf(48,plain,
double_divide(A,double_divide(double_divide(identity,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,37]),45,28]),
[iquote('para_into,25.1.1.2.2,37.1.1,demod,45,28')] ).
cnf(64,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),47,45]),
[iquote('back_demod,31,demod,47,45')] ).
cnf(83,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,37]),24,45]),
[iquote('para_into,33.1.1.1.2.2,37.1.1,demod,24,45')] ).
cnf(95,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[64]),83]),
[iquote('back_demod,64,demod,83')] ).
cnf(96,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(a2,identity)))) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),83]),
[iquote('back_demod,12,demod,83')] ).
cnf(99,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),B) = identity,
inference(para_from,[status(thm),theory(equality)],[33,11]),
[iquote('para_from,33.1.1,10.1.1.2')] ).
cnf(109,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(para_into,[status(thm),theory(equality)],[99,24]),
[iquote('para_into,99.1.1.1.2.2.2,23.1.1')] ).
cnf(128,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[109,33]),24,83])]),
[iquote('para_from,109.1.1,33.1.1.1.2.2,demod,24,83,flip.1')] ).
cnf(151,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(identity,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,24]),24]),
[iquote('para_into,48.1.1.2.1,23.1.1,demod,24')] ).
cnf(154,plain,
double_divide(identity,double_divide(identity,double_divide(A,double_divide(identity,A)))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,109]),83,128,95])]),
[iquote('para_into,48.1.1,109.1.1,demod,83,128,95,flip.1')] ).
cnf(160,plain,
double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[151])]),
[iquote('copy,151,flip.1')] ).
cnf(198,plain,
double_divide(double_divide(A,double_divide(identity,A)),identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[160,154]),24])]),
[iquote('para_into,160.1.1.2,154.1.1,demod,24,flip.1')] ).
cnf(250,plain,
double_divide(identity,double_divide(A,double_divide(identity,A))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[198,109]),24,24]),
[iquote('para_from,198.1.1,109.1.1.1.2.2,demod,24,24')] ).
cnf(258,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[250,33]),83]),
[iquote('para_from,250.1.1,33.1.1.1.2,demod,83')] ).
cnf(260,plain,
$false,
inference(binary,[status(thm)],[258,96]),
[iquote('binary,258.1,96.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP582-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:19:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.95 ----- Otter 3.3f, August 2004 -----
% 1.72/1.95 The process was started by sandbox on n027.cluster.edu,
% 1.72/1.95 Wed Jul 27 05:19:21 2022
% 1.72/1.95 The command was "./otter". The process ID is 18841.
% 1.72/1.95
% 1.72/1.95 set(prolog_style_variables).
% 1.72/1.95 set(auto).
% 1.72/1.95 dependent: set(auto1).
% 1.72/1.95 dependent: set(process_input).
% 1.72/1.95 dependent: clear(print_kept).
% 1.72/1.95 dependent: clear(print_new_demod).
% 1.72/1.95 dependent: clear(print_back_demod).
% 1.72/1.95 dependent: clear(print_back_sub).
% 1.72/1.95 dependent: set(control_memory).
% 1.72/1.95 dependent: assign(max_mem, 12000).
% 1.72/1.95 dependent: assign(pick_given_ratio, 4).
% 1.72/1.95 dependent: assign(stats_level, 1).
% 1.72/1.95 dependent: assign(max_seconds, 10800).
% 1.72/1.95 clear(print_given).
% 1.72/1.95
% 1.72/1.95 list(usable).
% 1.72/1.95 0 [] A=A.
% 1.72/1.95 0 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.72/1.95 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.72/1.95 0 [] inverse(A)=double_divide(A,identity).
% 1.72/1.95 0 [] identity=double_divide(A,inverse(A)).
% 1.72/1.95 0 [] multiply(identity,a2)!=a2.
% 1.72/1.95 end_of_list.
% 1.72/1.95
% 1.72/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.95
% 1.72/1.95 All clauses are units, and equality is present; the
% 1.72/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.95
% 1.72/1.95 dependent: set(knuth_bendix).
% 1.72/1.95 dependent: set(anl_eq).
% 1.72/1.95 dependent: set(para_from).
% 1.72/1.95 dependent: set(para_into).
% 1.72/1.95 dependent: clear(para_from_right).
% 1.72/1.95 dependent: clear(para_into_right).
% 1.72/1.95 dependent: set(para_from_vars).
% 1.72/1.95 dependent: set(eq_units_both_ways).
% 1.72/1.95 dependent: set(dynamic_demod_all).
% 1.72/1.95 dependent: set(dynamic_demod).
% 1.72/1.95 dependent: set(order_eq).
% 1.72/1.95 dependent: set(back_demod).
% 1.72/1.95 dependent: set(lrpo).
% 1.72/1.95
% 1.72/1.95 ------------> process usable:
% 1.72/1.95 ** KEPT (pick-wt=5): 1 [] multiply(identity,a2)!=a2.
% 1.72/1.95
% 1.72/1.95 ------------> process sos:
% 1.72/1.95 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.72/1.95 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.72/1.95 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.72/1.95 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.72/1.95 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.72/1.95 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.72/1.95 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.72/1.95 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.72/1.95 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.72/1.95 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.72/1.95 >>>> Starting back demodulation with 4.
% 1.72/1.95 >>>> Starting back demodulation with 6.
% 1.72/1.95 >> back demodulating 1 with 6.
% 1.72/1.95 >>>> Starting back demodulation with 8.
% 1.72/1.95 >>>> Starting back demodulation with 11.
% 1.72/1.95
% 1.72/1.95 ======= end of input processing =======
% 1.72/1.95
% 1.72/1.95 =========== start of search ===========
% 1.72/1.95
% 1.72/1.95 -------- PROOF --------
% 1.72/1.95
% 1.72/1.95 ----> UNIT CONFLICT at 0.01 sec ----> 260 [binary,258.1,96.1] $F.
% 1.72/1.95
% 1.72/1.95 Length of proof is 29. Level of proof is 12.
% 1.72/1.95
% 1.72/1.95 ---------------- PROOF ----------------
% 1.72/1.95 % SZS status Unsatisfiable
% 1.72/1.95 % SZS output start Refutation
% See solution above
% 1.72/1.95 ------------ end of proof -------------
% 1.72/1.95
% 1.72/1.95
% 1.72/1.95 Search stopped by max_proofs option.
% 1.72/1.95
% 1.72/1.95
% 1.72/1.95 Search stopped by max_proofs option.
% 1.72/1.95
% 1.72/1.95 ============ end of search ============
% 1.72/1.95
% 1.72/1.95 -------------- statistics -------------
% 1.72/1.95 clauses given 28
% 1.72/1.95 clauses generated 351
% 1.72/1.95 clauses kept 152
% 1.72/1.95 clauses forward subsumed 321
% 1.72/1.95 clauses back subsumed 5
% 1.72/1.95 Kbytes malloced 1953
% 1.72/1.95
% 1.72/1.95 ----------- times (seconds) -----------
% 1.72/1.95 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.72/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.95
% 1.72/1.95 That finishes the proof of the theorem.
% 1.72/1.95
% 1.72/1.95 Process 18841 finished Wed Jul 27 05:19:23 2022
% 1.72/1.95 Otter interrupted
% 1.72/1.95 PROOF FOUND
%------------------------------------------------------------------------------